What is the answer to log_{x}(1/x)=-1 ?

The answer to log_{x}(1/x)=-1 is 0 1

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log_{x}(1/x)=-1

lo g_{x} (\frac{1}{x}) = - 1

0 < x < 1 or x > 1

Solution steps

lo g_{x} (\frac{1}{x}) = - 1

Apply log rules

\frac{ln ( \frac{1}{x} )}{ln ( x )} = - 1

Multiply both sides by

ln (x)

\frac{ln ( \frac{1}{x} )}{ln ( x )} ln (x) = - 1 \cdot ln (x)

Apply log rules

- ln (x) = - ln (x)

Rewrite the equation with

ln (x) = u

- u = - u

Both sides are equal

True for all u

Verify Solutions:

0 < x < 1 or x > 1

The solution is

0 < x < 1 or x > 1

400 = 300 lo g_{10} (d) + 65

lo g_{3} (2 + x) - lo g_{3} (2 - x) = 3

lo g_{3} (x + 7) - lo g_{3} (x - 7) = 2

y, x = ln (2 y - 1)

3 lo g_{8} (2 x + 7) + 8 = 10

What is the answer to log_{x}(1/x)=-1 ?
The answer to log_{x}(1/x)=-1 is 0<x<1\lor x>1
Solve for x: log_{x}(1/x)=-1
The solution is 0<x<1\lor x>1